Asked Feb 13, 2019

What effect does standardizing into z-scores have on the spread (standard deviation) of a variable?


Expert Answer

Step 1

What is Z-score and standardized variables:


The Z-score measures a particular value’s relationship to the mean in a group of values. It gives the number of standard deviation from the mean for the particular data point.

The general formula to obtain Z-score is,

Z = (x – population mean) / population standard deviation.

Standardized variables:

Standardized variables are the variables which are rescaled using the Z-score and these variables will have mean 0 and standard deviation 1.

Step 2

Find the effect of standardizing into z-scores on the spread of a variable:

From the definition of z-score and standardized variables, it is known that the standard deviation of the standardized variable will be equal to “1”.

That is, standardizing into z-scores changes the spread by making standard deviation as 1. Since, the units of the variable...

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